Questions and Answers
What is the difference between scalars and vectors?
Scalars are physical quantities with only magnitude, while vectors have both magnitude and direction.
How are vectors represented analytically?
Vectors are represented analytically by a letter with an arrow over its head or with bold face letter.
Which method is used to represent vectors by drawing a straight line with an arrow to scale?
Vector addition is not simple algebraic addition, it obeys the laws of vector addition. The resultant of two vectors having the same direction is the ________ of the two vectors.
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How is the direction of the resultant vector determined when two vectors act at right angles to each other?
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What are the types of forces according to Chapter Four: Dynamics? (Select all that apply)
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Angular position, angular velocity, and angular acceleration are topics covered in which chapter?
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What is the type of motion discussed in Chapter Six?
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______ is the law discussed in Chapter Eight related to electric charges.
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Match the following topics with the correct chapter in the physics module:
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What is the equation representing angular momentum according to Eqn. 3.6?
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What does Eqn. 3.7 represent?
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What is the condition for two or more vectors to be equal?
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What are the units for the gravitational constant G?
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What is the formula for calculating the magnitude and direction of the car's resultant displacement?
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In dynamics, what are the fundamental concepts that are described by Newton's laws of motion?
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What are the components of a vector in a threedimensional space?
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What is a unit vector and how is it represented?
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Explain the scalarvector multiplication and provide one rule associated with it.
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What is the formula for the dot product of two vectors A and B?
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What is the result of the cross product of vector A = (ax î + ay ĵ + az k̂) and vector B = (bx î + by ĵ + bz k̂)?
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What is the freefall acceleration on the planet where an astronaut can jump a maximum horizontal distance of 15.0m with an initial speed of 3.00m/s?
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What is the term used to describe the acceleration that is always toward the center of a circle, perpendicular to velocity?
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What is the time taken for one complete rotation known as?
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What is the unit of angular displacement?
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How is average angular velocity defined?
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What is the equation that describes the relationship for uniformly accelerated angular motion?
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What quantity is expressed as a cross product of distance from the axis of rotation and linear momentum?
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What does the moment of inertia of a body depend on?
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Define Torque.
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What factors does the magnitude of torque depend on?
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What is the formula for calculating torque?
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An electron in a cathode ray tube accelerates uniformly from 2.0 x 10^4 m/s to 6.0 x 10^6 m/s over 1.5 cm. How long does the electron take to travel this 1.5 cm?
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An electron in a cathode ray tube accelerates uniformly from 2.0 x 10^4 m/s to 6.0 x 10^6 m/s over 1.5 cm. What is its acceleration?
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A track covers 40m in 8.5s while smoothly slowing down to a final speed of 2.8m/s. What is its original velocity?
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A track covers 40m in 8.5s while smoothly slowing down to a final speed of 2.8m/s. What is its acceleration?
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A car traveling at a constant speed of 45m/s passes a trooper hidden behind a billboard. One second after the car passes, the trooper sets out to catch it at an acceleration of 3.0m/s^2. How long does it take for the trooper to overtake the car?
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A jet lands on an aircraft at 140 mi/hr and stops in 2s due to an arresting cable. What is its acceleration?
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A jet lands on an aircraft at 140 mi/hr and stops in 2s due to an arresting cable. If the jet touches down at position xi = 0, what is the final position of the plane?
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A jet plane lands with a speed of 100 m/s and slows down at a rate of 5 m/s^2. What is the time interval needed for the jet to come to rest?
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A jet plane lands with a speed of 100 m/s and slows down at a rate of 5 m/s^2. Can this jet land on an airport where the runway is 0.8 km long?
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What is the mathematical expression of the restoring force dependent on?
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What is the defining property of linear momentum?
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Linear momentum is the product of mass of the system with its ________.
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Linear momentum is a scalar quantity.
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What is impulse defined as?
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Match the following collision types with their descriptions:
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Which of the following statements is true about the relationship between the dot product of two vectors and the product of the magnitudes of the vectors?
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Which of the following is equivalent to the scalar product: (A ~ × ~A) • ~B?
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Which of the following statements is true about the relationship between the magnitude of the cross product of two vectors and the product of the magnitudes of the vectors?
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Is the triple product defined by A • (B × C) a scalar or a vector quantity?
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What are the directions of (a) A × B and (b) B × A if vector A is in the negative y direction and vector B is in the negative x direction?
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Calculate the M • N, M × N, and the angle between M and N given M = 6î + 2ĵ  k̂ and N = 2î  ĵ  3k̂.
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Study Notes
Vectors
 Scalar quantities: physical quantities with only magnitude, e.g., electric charge, density, mass
 Vector quantities: physical quantities with both magnitude and direction, e.g., velocity, force, torque, electric field
Vector Representation
 Analytical methods: represented by a letter with an arrow over its head or with bold face letter, e.g., →F or F, →P or P, →A or A
 Graphical/Geometrical methods: represented by a straight line with an arrow, where length is the magnitude and arrow direction is the direction
Vector Addition and Subtraction
 Resultant vector (R): the sum of two or more vectors
 Vector subtraction: addition of the negative vector, e.g., →R = →A  →B = →A + (→B)

Vector addition laws:
 The resultant of two vectors with the same direction is the algebraic sum of the two vectors with the same direction as both.
 Not commutative: order of vectors matters, e.g., →A + →B ≠ →B + →A
 Associative: (→A + →B) + →C = →A + (→B + →C)
Key Concepts
 Magnitude: the size or amount of a vector
 Direction: the orientation or direction of a vectorHere are the study notes for the text:
Kinematics
 Definition: Kinematics is a branch of mechanics that describes the motion of an object without reference to the cause of motion (force).
One or Two Dimensional (2D) Motion
 Motion: Continuous change of position with time.
 Position: Location of an object with respect to a chosen reference frame or point.
 Reference Frame: A system of graduated lines symbolically attached to a body that serves to describe the position of points relative to the body.
Types of Motion

Translational Motion: When all points of an object move the same distance in a given time.
 Rectilinear motion: Object moves in a straight line (e.g. car moving in a straight line, bullet being fired).
 Curvilinear motion: Object moves along a curved path (e.g. child going down a slide, bird flying in the sky).

Rotational Motion: When an object moves about an axis and different parts of it move by different distances in a given interval of time.
 Examples: Blades of a rotating fan, merrygoround, blades of a windmill.

Vibrational Motion: When a body moves to and fro about its mean position.
 Examples: Pendulums, swings, tuning forks.
Let me know if this meets your requirements!### Vibrational Motion
 Vibrational motion can be periodic or nonperiodic
Kinematics of the Particle
Motion in 1D
 Motion of a particle along a straight line in a fixed direction (or motion along one coordinate axis)
 Example: a car moving along a flat straight narrow road
Kinematical Terms
 Distance: total path length covered by the moving object
 Displacement: change of position (shortest distance between start and end of motion)
 Speed: rate of change of distance in a unit time
 Average Speed: total distance traveled by the total time required to cover the distance
 Velocity: rate of change of displacement as a function of time
 Average Velocity: change of displacement divided by the time interval during which the displacement occurs
 Instantaneous Velocity: velocity of the particle at a given instant of time (limit of average velocity as Δt approaches to zero)
 Instantaneous Speed: magnitude of instantaneous velocity
Acceleration
 Acceleration: rate of change of velocity
 Average Acceleration: change in velocity divided by the time interval during which the change in velocity occurs
 Instantaneous Acceleration: acceleration of the particle at a given instant of time (limit of average acceleration as Δt approaches to zero)
Uniform Motion in 1D
 Uniform Motion: equal distances traveled in equal intervals of time
 Acceleration: zero
 Velocity: remains constant
 Speed: equal to the actual speed
 Instantaneous Velocity: equal to the actual velocity
Uniformly Accelerated Motion in 1D
 Uniformly Accelerated Motion: motion with constant acceleration
 Velocity: changes with uniform rate

Equations of Motion:
 v(t) = vi + at
 ∆x = vi t + (1/2) at^2
 v^2 = vi^2 + 2a∆x
Free Falling Bodies
 Free Falling Bodies: objects moving freely under the influence of gravity alone

Equations of Motion:
 vy = gt
 ∆y = (1/2) gt^2
 vy^2 = 2g∆y
TwoDimensional Motion
 TwoDimensional Motion: motion in a plane (two coordinate axes simultaneously)
 Displacement: ∆~r = ~rB  ~rA
 Average Velocity: ~vav = ∆~r / ∆t
 Instantaneous Velocity: v(t) = lim (∆~r / ∆t) as Δt approaches to zero
 Average Acceleration: ~aav = ∆~v / ∆t
 Instantaneous Acceleration: a(t) = lim (∆~v / ∆t) as Δt approaches to zero
Projectile Motion
 Projectile Motion: motion of an object in a plane under the influence of gravity alone
 Trajectory: parabolic path
 Horizontal Motion: uniform motion (ax = 0)
 Vertical Motion: uniformly accelerated motion (ay = g)

Equations of Motion:
 x(t) = v0x t
 y(t) = v0y t  (1/2) gt^2
 v0y = v0 sinθ
 ymax = v0y^2 / 2g
 t = 2v0y / g
 R = v0^2 sin(2θ) / g
Circular Motion
 Circular Motion: motion in a circular path at a constant speed
 Uniform Circular Motion: constant speed and direction
 Velocity: not constant due to continuous change in direction
 Acceleration: radial acceleration (a = v^2 / r)
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Description
This quiz is a part of the PreUniversity Remedial Program for the 2014 E.C.ESSLCE exam in Ethiopia, covering the Physics Module, specifically vectors and scalar quantities.